題目

Mahmoud wants to send a message to his friend Ehab. Their language consists of n words numbered from 1 to n. Some words have the same meaning so there are k groups of words such that all the words in some group have the same meaning.

Mahmoud knows that the i-th word can be sent with cost ai. For each word in his message, Mahmoud can either replace it with another word of the same meaning or leave it as it is. Can you help Mahmoud determine the minimum cost of sending the message?

The cost of sending the message is the sum of the costs of sending every word in it.

Input

The first line of input contains integers n, k and m (1 ≤ k ≤ n ≤ 105, 1 ≤ m ≤ 105) — the number of words in their language, the number of groups of words, and the number of words in Mahmoud’s message respectively.

The second line contains n strings consisting of lowercase English letters of length not exceeding 20 which represent the words. It’s guaranteed that the words are distinct.

The third line contains n integers a1, a2, …, an (1 ≤ ai ≤ 109) where ai is the cost of sending the i-th word.

The next k lines describe the groups of words of same meaning. The next k lines each start with an integer x (1 ≤ x ≤ n) which means that there are x words in this group, followed by x integers which represent the indices of words in this group. It’s guaranteed that each word appears in exactly one group.

The next line contains m space-separated words which represent Mahmoud’s message. Each of these words appears in the list of language’s words.

Output

The only line should contain the minimum cost to send the message after replacing some words (maybe none) with some words of the same meaning.

Examples

input

5 4 4
i loser am the second
100 1 1 5 10
1 1
1 3
2 2 5
1 4
i am the second

output

107

input

5 4 4
i loser am the second
100 20 1 5 10
1 1
1 3
2 2 5
1 4
i am the second

output

116

Note

In the first sample, Mahmoud should replace the word “second” with the word “loser” because it has less cost so the cost will be 100+1+5+1=107.

In the second sample, Mahmoud shouldn’t do any replacement so the cost will be 100+1+5+10=116.

題意：

Mahmoud傳送訊息給好友，每個訊息包含多個字串，傳送訊息中的每個字串需要花費一定的費用，但是其中有些字串所表達的含義一樣，可以互相替換，求傳送訊息的最小費用。

解題思路：

建立一個HashMap集合，將每個字串作為鍵值，能互相交換的的字串其鍵值對應的值為相同的傳送價格值的下標，然後將字串的價格存入在陣列中，如果有可以替換的字串，比較其價格，將花費最小的值存入陣列中。因為HashMap的鍵值所對應的值就是其在花費的陣列的下標。最後通過輸入要傳送字串（即HashMap的鍵值）找到HashMap鍵值所對應值即花費陣列的下表，將價格累加即可。

AC–Code

import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int m =sc.nextInt();
		String[] s = new String[n];
		for(int i=0 ;i<n;i++)
		{
			s[i] = sc.next();
		}
		int[] d = new int[n];
		for(int i = 0;i<n;i++)
		{
			d[i] = sc.nextInt();
		}
		HashMap<String, Integer> map = new HashMap<String,Integer>();
		int[] min = new int[k];
		Arrays.fill(min,Integer.MAX_VALUE);
		for(int i =0;i<k;i++)
		{
			int count = sc.nextInt();
			while(count-->0)
			{
				int x = sc.nextInt()-1;
				map.put(s[x],i);
				min[i] = Math.min(min[i], d[x]);
			}
		}
		long p = 0;
		for(int i = 0;i<m;i++)
		{
			p+=min[map.get(sc.next())];
		}
		System.out.println(p);
		sc.close();
	}
}